Hello, s_ingram!
Find the equations of the two circles which pass through the point (2,0)
and have both the axis and the line as tangents. Code:

 R
 +  P  * o *    y=1
+o:*
 * 2 : *
* : *
 :
* : *
Q o     o C *
* (x,y) *

* *
 * *
 * *
 * * *

The center of the circle is
It passes through the point
It is tangent to the axis at
It is tangent to at
The radius is: .
We have: .
Since , then: .
Since , we have: .
. . which becomes: .
Then: .
. . which simplifies to: .
. . which factors: .
. . and has roots: .
. . . . . . . . Then: .
One circle has center and
The other has center and